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A coupled PFEM–Eulerian approach for the solution of porous FSI problems

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Abstract

This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a Lagrangian model for the structural behavior and an Eulerian approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an Eulerian fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.

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References

  1. Adam D, Wood W (1983) Comparison of Hilber–Hughes–Taylor and Bossak α methods for the numerical integration of vibration equations. Int J Numer Methods Eng 19: 765–771

    Article  Google Scholar 

  2. Biot M (1941) General theory of three dimensional consolidation. J Appl Phys 12: 155–164

    Article  MATH  Google Scholar 

  3. de Boer R (2000) Theory of porous media. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Carbonell J, Oñate E, Suárez B (2008) Modeling of ground exavation with the particle finite element method (pfem). ASCE J Eng Mech 136: 455–463

    Article  Google Scholar 

  5. Codina R (2000) A nodal-based implementation of a stabilized finite element method for incompressible flow problems. Int J Numer Methods Fluids 33: 737–766

    Article  MathSciNet  MATH  Google Scholar 

  6. Codina R (2000) Pressure stability in fractional step finite element methods for incompressible flows. J Comput Phys 170: 112–140

    Article  MathSciNet  Google Scholar 

  7. Codina R, Soto O (2004) Approximation of the incompressible Navier-Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes. Comput Methods Appl Mech Eng 193: 1403–1419

    Article  MathSciNet  MATH  Google Scholar 

  8. Cremonesi M, Frangi A, Perego U (2011) A lagrangian finite element approach for the simulation of water-waves induced by landslides. Comput Struct 89: 1086–1093

    Article  Google Scholar 

  9. Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17: 253–297

    Article  MATH  Google Scholar 

  10. Hsu MC, Bazilevs Y, Calo V, Tezduyar TE, Hughes T (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199: 828–840

    Article  MathSciNet  MATH  Google Scholar 

  11. ICOLD (1995) Bulletin 99, dam failures statistical analysis. ICOLD, Paris

  12. Larese A (2012) A coupled Eulerian–PFEM model for the simulation of overtopping in rockfill dams. PhD Thesis. Universitat Politècnica de Catalunya. UPC BarcelonaTech, Barcelona

  13. Larese A, Rossi R, Oñate E, Idelsohn S (2008) Validation of the particle finite element method (PFEM) for simulation of free surface flows. Eng Comput 25: 385–425

    Article  Google Scholar 

  14. Lewis R, Schrefler B (1998) The finite element method for the static and dynamic deformation and consolidation of porous media. Wiley, New York

    Google Scholar 

  15. Lipscomb G, Denn M (1984) Flow of a bingham fluid in complex geometries. J Non Newtonian Fluid Mech 14: 337–346

    Article  MATH  Google Scholar 

  16. Marti J, Ryzhakov P, Idelsohn S, Oñate E (2012) Combined Eulerian–PFEM approach for analysis of polymers in fire situations. Int J Numer Methods Eng 81(2): 135–268

    Google Scholar 

  17. Mier M, Idelsohn S, Oñate E (2010) Advances in the simulation of multi-fluid flows with the particle finite element method. Int J Numer Methods Fluids 67: 1516–1539

    Article  Google Scholar 

  18. Mossaiby F, Rossi R, Dadvand P, Idelsohn S (2011) OpenCL-based implementation of an unstructured edge-based finite element convection–diffusion solver on graphics hardware. Int J Numer Methods Eng 89(13): 1635

    Article  Google Scholar 

  19. Nield D, Bejan A (1992) Convection in porous media. Springer, New York

    Google Scholar 

  20. Nithiarasu P, Seetharamu K, Sundararajan T (1997) Natural convective heat transfer in a fluid saturated variable porosity medium. Int J Heat Mass Transf 40: 3955–3967

    Article  MATH  Google Scholar 

  21. Coussy O (1995) Mechanics of porous media. Wiley, New York

    Google Scholar 

  22. Oñate E, Celigueta M, Idelsohn S, Salazar F, Suarez B (2011) Possibilities of the particle finite element method for fluid–soil-structure interaction problems. J Comput Mech 48: 307–318

    Article  MATH  Google Scholar 

  23. Oñate E, Idelsohn S, Celigueta M, Rossi R (2008) Advances in the particle finite element method for the analysis of fluid multibody interaction and bed erosion in free surface flows. Comput Methods Appl Mech Eng 197: 1777–1800

    Article  MATH  Google Scholar 

  24. Oñate E, Idelsohn S, Celigueta M, Rossi R, Marti J, Carbonell J, Ryzakov P, Suárez B (2011) Advances in the particle finite element method (PFEM) for solving coupled problems in engineering. In: Oñate E, Owen R (eds) Particle-based methods, computational methods in applied sciences, vol 25. Springer, New York

  25. Oñate E, Idelsohn S, Pin FD, Aubry R (2004) The particle finite element method an overview. Int J Comput Methods 1: 267–307

    Article  MATH  Google Scholar 

  26. Osher S, Fedkiw RP (2003) Level set methods and dynamic implicit surfaces. Springer, New York

    MATH  Google Scholar 

  27. Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31: 385–404

    Article  MATH  Google Scholar 

  28. Quecedo M, Pastor M, Herreros M, Merodo JF (2004) Numerical modelling of the propagation of fast landslides using the finite element method. Int J Numer Methods Eng 59: 755–794

    Article  MATH  Google Scholar 

  29. Rojek J, Labra C, Su O, Oñate E (2012) Comparative study of different discrete element models and evaluation of equivalent micromechanical parameters. Int J Solids Struct 49: 1497–1517

    Article  Google Scholar 

  30. Rossi R, Larese A, Dadvand P, Oñate E (2012) An efficient edge-based level set finite element method for free surface flow problems. Int J Numer Methods Fluids. doi:10.1002/fld.3680

  31. Ryzhakov P, Rossi R, Idelsohn S, Oñate E (2010) A monolithic lagrangian approach for fluid-structure interaction problems. Int J Comput Mech 46(6): 883–899

    Article  MATH  Google Scholar 

  32. Ryzhakov P, Rossi R, Oñate E (2011) An algorithm for the simulation of thermally coupled low speed flow problems. Int J Numer Methods Fluids 65: 1217–1230

    Article  Google Scholar 

  33. Soto O, Lohner R, Cebral J, Camelli F (2004) A stabilized edge-based implicit incompressible flow formulation. Comput Methods Appl Mech Eng 193: 2139–2154

    Article  MATH  Google Scholar 

  34. Taylor D (1948) Fundamentals of soil mechanics. Wiley, New York

    Google Scholar 

  35. Tezduyar T (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44

    Article  MathSciNet  MATH  Google Scholar 

  36. Tezduyar T (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575

    Article  MathSciNet  MATH  Google Scholar 

  37. Tezduyar T, Osawa Y (2000) Finite element stabilization parameters computed for element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430

    Article  MATH  Google Scholar 

  38. Toledo M (1997) Presas De Escollera Sometidas a Sobrevertido. Estudio del Movimientos dal Agua a Través de la Escollera e de la Estabilidad Frente al Deslizamiento en Masa. PhD thesis: Universidad Politécnica de Madrid

  39. Wellmann C, Wriggers P (2012) A two-scale model of granular materials. Comput Methods Appl Mech Eng 1: 46–58

    Article  MathSciNet  Google Scholar 

  40. Zienkiewicz O, Chan A, Pastor M, Schrefler B, Shiomi T (1999) Computational geomechanics with special reference to earthquake engineering. Wiley, New York

    MATH  Google Scholar 

  41. Zienkiewicz O, Shiomi T (1984) Dynamic behaviour of saturated porous media: the generalised biot formulation and its numerical solution. Int J Numer Anal Methods Geomech 8: 71–96

    Article  MATH  Google Scholar 

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Larese, A., Rossi, R., Oñate, E. et al. A coupled PFEM–Eulerian approach for the solution of porous FSI problems. Comput Mech 50, 805–819 (2012). https://doi.org/10.1007/s00466-012-0768-9

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  • DOI: https://doi.org/10.1007/s00466-012-0768-9

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